On variant strategies to solve the magnitude least squares optimization problem in parallel transmission pulse design and under strict SAR and power constraints

Local SAR management strategies to use two-channel RF shimming for fetal MRI at 3 T

PURPOSE

This study evaluates the imaging performance of two-channel RF-shimming for fetal MRI at 3 T using four different local specific absorption rate (SAR) management strategies.

METHODS

Due to the ambiguity of safe local SAR levels for fetal MRI, local SAR limits for RF shimming were determined based on either each individual's own SAR levels in standard imaging mode (CP mode) or the maximum SAR level observed across seven pregnant body models in CP mode. Local SAR was constrained either indirectly by further constraining the whole-body SAR (wbSAR) or directly by using subject-specific local SAR models. Each strategy was evaluated by the improvement of the transmit field efficiency (average |B1 + |) and nonuniformity (|B1 + | variation) inside the fetus compared with CP mode for the same wbSAR.

RESULTS

Constraining wbSAR when using RF shimming decreases B1 + efficiency inside the fetus compared with CP mode (by 12%-30% on average), making it inefficient for SAR management. Using subject-specific models with SAR limits based on each individual's own CP mode SAR value, B1 + efficiency and nonuniformity are improved on average by 6% and 13% across seven pregnant models. In contrast, using SAR limits based on maximum CP mode SAR values across seven models, B1 + efficiency and nonuniformity are improved by 13% and 25%, compared with the best achievable improvement without SAR constraints: 15% and 26%.

CONCLUSION

Two-channel RF-shimming can safely and significantly improve the transmit field inside the fetus when subject-specific models are used with local SAR limits based on maximum CP mode SAR levels in the pregnant population.

What can we gain from subpopulation universal pulses? A simulation-based study

PURPOSE

The aim of the study was to explore a novel methodology for designing universal pulses (UPs) that balances the benefits of a calibration-free approach with subject-specific online pulse design.

METHODS

The proposed method involves segmenting the population into subpopulations with variability in anatomical shapes and positions reduced to 75%, 50%, and 25% of their original values while keeping the mean values unchanged. An additional 25% extreme case with a large volume of interest and shifted position was included. For each group, a 5kT-points universal inversion pulse was designed and assessed by the normalized root mean square error (NRMSE) on the target longitudinal magnetization profile. The performance was compared to the conventional one-size-fits-all approach. A total of 132 electromagnetic simulations were executed to generate representative anatomies and specific absorption rate (SAR) distributions in a three-dimensional parameter space comprised of head breadth, head length, and Y-shift. The 99.9th percentile on the peak local SAR distribution was utilized to establish an intersubject variability safety margin.

RESULTS

UPs designed for subpopulations with decreased head shape and position variability reduced the anatomical safety margin by up to 20%. Furthermore, when a head was significantly different to the average case, the proposed approach improved the inversion homogeneity by up to 24%, compared to the conventional one-size-fits-all approach.

CONCLUSION

Subpopulation UPs present an opportunity to improve theB 1 + $$ {\mathrm{B}}_1^{+} $$ homogeneity and reduce anatomical SAR safety margins at 7T without additional acquisition time for calibration.

Technical note: Multi-receiver combination method for phase-based electrical property tomography of the breast

BACKGROUND

Phase-based electrical property tomography (EPT) is a technique that allows conductivity reconstruction with only phase of the B₁ field under the assumption that the magnitude of the B₁ fields are homogeneous. The more this assumption is violated, the less accurate the reconstructed conductivity. Thus, a method that ensures homogeneity of | B 1 - | $| {{\rm{B}}_1^ - } |$ field is important for breast image using multi-receiver coil.

PURPOSE

To develop a method for multi-receiver combination for phase-based EPT usable for breast EPT imaging in the clinic.

METHODS

Theory of the proposed method is presented. To validate the proposed method, the phantom and in-vivo experiments were conducted. Conductivity images were reconstructed using the transceive phase of the combined image and results were compared with another combination method.

RESULTS

The proposed method's conductivity results were more stable than those of the previous method when | B 1 + | $| {{\rm{B}}_1^ + } |$ was not homogeneous and when the homogeneous contrast region was small. The phantom and in-vivo results indicate that the proposed method produces improved conductivity images than the previous method. The proposed combination method also increased the conductivity contrast between benign and cancerous tissues.

CONCLUSION

The proposed method produced more stable multi-receiver combination for phase-based EPT of the breast in a clinical environment.

Parallel transmission 2D RARE imaging at 7T with transmit field inhomogeneity mitigation and local SAR control

PURPOSE

We develop and test a parallel transmit (pTx) pulse design framework to mitigate transmit field inhomogeneity with control of local specific absorption rate (SAR) in 2D rapid acquisition with relaxation enhancement (RARE) imaging at 7T.

METHODS

We design large flip angle RF pulses with explicit local SAR constraints by numerical simulation of the Bloch equations. Parallel computation and analytical expressions for the Jacobian and the Hessian matrices are employed to reduce pulse design time. The refocusing-excitation "spokes" pulse pairs are designed to satisfy the Carr-Purcell-Meiboom-Gill (CPMG) condition using a combined magnitude least squares-least squares approach.

RESULTS

In a simulated dataset, the proposed approach reduced peak local SAR by up to 56% for the same level of refocusing uniformity error and reduced refocusing uniformity error by up to 59% (from 32% to 7%) for the same level of peak local SAR compared to the circularly polarized birdcage mode of the pTx array. Using explicit local SAR constraints also reduced peak local SAR by up to 46% compared to an RF peak power constrained design. The excitation and refocusing uniformity error were reduced from 20%-33% to 4%-6% in single slice phantom experiments. Phantom experiments demonstrated good agreement between the simulated excitation and refocusing uniformity profiles and experimental image shading.

CONCLUSION

PTx-designed excitation and refocusing CPMG pulse pairs can mitigate transmit field inhomogeneity in the 2D RARE sequence. Moreover, local SAR can be decreased significantly using pTx, potentially leading to better slice coverage, enabling larger flip angles or faster imaging.

Bench to bore ramifications of inter-subject head differences on RF shimming and specific absorption rates at 7T

PURPOSE

This study shows how inter-subject variation over a dataset of 72 head models results in specific absorption rate (SAR) and B₁⁺ field homogeneity differences using common shim scenarios.

METHODS

MR-CT datasets were used to segment 71 head models into 10 tissue compartments. These head models were affixed to the shoulders and neck of the virtual family Duke model and placed within an 8 channel transmit surface-loop array to simulate the electromagnetic fields of a 7T imaging experiment. Radio frequency (RF) shimming using the Gerchberg-Saxton algorithm and Circularly Polarized shim weights over the entire brain and select slices of each model was simulated. Various SAR metrics and B₁⁺ maps were calculated to demonstrate the contribution of head variation to transmit inhomogeneity and SAR variability.

RESULTS

With varying head geometries the loading for each transmit loop changes as evidenced by changes in S-parameters. The varying shim conditions and head geometries are shown to affect excitation uniformity, spatial distributions of local SAR, and SAR averaging over different pulse sequences. The Gerchberg-Saxton RF shimming algorithm outperforms circularly polarized shimming for all head models. Peak local SAR within the coil most often occurs nearest the coil on the periphery of the body. Shim conditions vary the spatial distribution of SAR.

CONCLUSION

The work gives further support to the need for fast and more subject specific SAR calculations to maintain safety. Local SAR_10g is shown to vary spatially given shim conditions, subject geometry and composition, and position within the coil.

OTUP workflow: target specific optimization of the transmit k-space trajectory for flexible universal parallel transmit RF pulse design

PURPOSE

To optimize transmit k-space trajectories for a wide range of excitation targets and to design "universal pTx RF pulses" based on these trajectories.

METHODS

Transmit k-space trajectories (stack of spirals and SPINS) were optimized to best match different excitation targets using the parameters of the analytical equations of spirals and SPINS. The performances of RF pulses designed based on optimized and non-optimized trajectories were compared. The optimized trajectories were utilized for universal pulse design. The universal pulse performances were compared with subject specific tailored pulse performances. The OTUP workflow (optimization of transmit k-space trajectories and universal pulse calculation) was tested on three test target excitation patterns. For one target (local excitation of a central area in the human brain) the pulses were tested in vivo at 9.4 T.

RESULTS

The workflow produced appropriate transmit k-space trajectories for each test target. Utilization of an optimized trajectory was crucial for the pulse performance. Using unsuited trajectories diminished the performance. It was possible to create target specific universal pulses. However, not every test target is equally well suited for universal pulse design. There was no significant difference in the in vivo performance between subject specific tailored pulses and a universal pulse at 9.4 T.

CONCLUSIONS

The proposed workflow further exploited and improved the universal pulse concept by combining it with gradient trajectory optimization for stack of spirals and SPINS. It emphasized the importance of a well suited trajectory for pTx RF pulse design. Universal and tailored pulses performed with a sufficient degree of similarity in simulations and a high degree of similarity in vivo. The implemented OTUP workflow and the B₀ /B₁⁺ map data from 18 subjects measured at 9.4 T are available as open source (https://github.com/ole1965/workflow_OTUP.git).

Mitigating transmit‐B 1 artifacts by predicting parallel transmission images with deep learning: A feasibility study using high‐resolution whole‐brain diffusion at 7 Tesla

Purpose

To propose a novel deep learning (DL) approach to transmit‐B₁ (B₁⁺)‐artifact mitigation without direct use of parallel transmission (pTx), by predicting pTx images from single‐channel transmission (sTx) images.

Methods

A deep encoder–decoder convolutional neural network was constructed and trained to learn the mapping from sTx to pTx images. The feasibility was demonstrated using 7 T Human‐Connectome Project (HCP)‐style diffusion MRI. The training dataset comprised images acquired on 5 healthy subjects using commercial Nova RF coils. Relevant hyperparameters were tuned with a nested cross‐validation, and the generalization performance evaluated using a regular cross‐validation.

Results

Our DL method effectively improved the image quality for sTx images by restoring the signal dropout, with quality measures (including normalized root‐mean‐square error, peak SNR, and structural similarity index measure) improved in most brain regions. The improved image quality was translated into improved performances for diffusion tensor imaging analysis; our method improved accuracy for fractional anisotropy and mean diffusivity estimations, reduced the angular errors of principal eigenvectors, and improved the fiber orientation delineation relative to sTx images. Moreover, the final DL model trained on data of all 5 subjects was successfully used to predict pTx images for unseen new subjects (randomly selected from the 7 T HCP database), effectively recovering the signal dropout and improving color‐coded fractional anisotropy maps with largely reduced noise levels.

Conclusion

The proposed DL method has potential to provide images with reduced B1⁺ artifacts in healthy subjects even when pTx resources are inaccessible on the user side.

Personalized local SAR prediction for parallel transmit neuroimaging at 7T from a single T1-weighted dataset

Purpose

Parallel RF transmission (PTx) is one of the key technologies enabling high quality imaging at ultra‐high fields (≥7T). Compliance with regulatory limits on the local specific absorption rate (SAR) typically involves over‐conservative safety margins to account for intersubject variability, which negatively affect the utilization of ultra‐high field MR. In this work, we present a method to generate a subject‐specific body model from a single T1‐weighted dataset for personalized local SAR prediction in PTx neuroimaging at 7T.

Methods

Multi‐contrast data were acquired at 7T (N = 10) to establish ground truth segmentations in eight tissue types. A 2.5D convolutional neural network was trained using the T1‐weighted data as input in a leave‐one‐out cross‐validation study. The segmentation accuracy was evaluated through local SAR simulations in a quadrature birdcage as well as a PTx coil model.

Results

The network‐generated segmentations reached Dice coefficients of 86.7% ± 6.7% (mean ± SD) and showed to successfully address the severe intensity bias and contrast variations typical to 7T. Errors in peak local SAR obtained were below 3.0% in the quadrature birdcage. Results obtained in the PTx configuration indicated that a safety margin of 6.3% ensures conservative local SAR estimates in 95% of the random RF shims, compared to an average overestimation of 34% in the generic “one‐size‐fits‐all” approach.

Conclusion

A subject‐specific body model can be automatically generated from a single T1‐weighted dataset by means of deep learning, providing the necessary inputs for accurate and personalized local SAR predictions in PTx neuroimaging at 7T.

Wireless Electromagnetic Radiation Assessment Based on the Specific Absorption Rate (SAR): A Review Case Study

Employing electromagnetic fields (EMFs) in new wireless communication and sensing technologies has substantially increased the level of human exposure to EMF waves. This paper presents a useful insight into the interaction of electromagnetic fields with biological media that is defined by the heat generation due to induced currents and dielectric loss. The specific absorption rate (SAR) defines the heating amount in a biological medium that is irradiated by an electromagnetic field value. The paper reviews the radio frequency hazards due to the SAR based on various safety standards and organisations, including a detailed investigation of previously published work in terms of modelling and measurements. It also summarises the most common techniques utilised between 1978 and 2021, in terms of the operational frequency spectrum, bandwidth, and SAR values.

B1 field map synthesis with generative deep learning used in the design of parallel-transmit RF pulses for ultra-high field MRI

Spoke trajectory parallel transmit (pTX) excitation in ultra-high field MRI enables B₁⁺ inhomogeneities arising from the shortened RF wavelength in biological tissue to be mitigated. To this end, current RF excitation pulse design algorithms either employ the acquisition of field maps with subsequent non-linear optimization or a universal approach applying robust pre-computed pulses. We suggest and evaluate an intermediate method that uses a subset of acquired field maps combined with generative machine learning models to reduce the pulse calibration time while offering more tailored excitation than robust pulses (RP). The possibility of employing image-to-image translation and semantic image synthesis machine learning models based on generative adversarial networks (GANs) to deduce the missing field maps is examined. Additionally, an RF pulse design that employs a predictive machine learning model to find solutions for the non-linear (two-spokes) pulse design problem is investigated. As a proof of concept, we present simulation results obtained with the suggested machine learning approaches that were trained on a limited data-set, acquired in vivo. The achieved excitation homogeneity based on a subset of half of the B₁⁺ maps acquired in the calibration scans and half of the B₁⁺ maps synthesized with GANs is comparable with state of the art pulse design methods when using the full set of calibration data while halving the total calibration time. By employing RP dictionaries or machine-learning RF pulse predictions, the total calibration time can be reduced significantly as these methods take only seconds or milliseconds per slice, respectively.

Standardized universal pulse: A fast RF calibration approach to improve flip angle accuracy in parallel transmission

PURPOSE

In parallel transmission (pTX), subject-tailored RF pulses allow achieving excellent flip angle (FA) accuracy but often require computationally extensive online optimizations, precise characterization of the static field ( Δ B 0 ), and the transmit RF field ( B 1 + ) distributions. This costs time and requires expertise from the MR user. Universal pulses (UPs) have been proposed to reduce this burden, yet, with a penalty in FA accuracy. This study introduces the concept of standardized universal pulses (SUPs), where pulses are designed offline and adjusted to the subject through a fast online calibration scan.

METHODS

A SUP is designed offline using a so-called standardized database, wherein each B 1 + map has been normalized to a reference transmit RF field distribution. When scanning a new subject, a 3-slice B 1 + acquisition (scan time < 10  s) is performed and used to adjust the SUP to the subject through a linear transform. SUP performance was assessed at 7T with simulations by computing the FA-normalized root mean square error (FA-NRMSE) and the FA pattern stability as measured by the average and coefficient of variation of the FA across 15 control subjects, along with in vivo experiments using an MP2RAGE sequence implementing the SUP variant for the FLASH readout.

RESULTS

Adjusted SUP improved the FA-NRMSE (8.8 % for UP vs. 7.1 % for adjusted SUP). Experimentally in vivo, this translated in an improved signal homogeneity and more accurate T 1 quantification using MP2RAGE.

CONCLUSION

The proposed SUP approach improves excitation accuracy (FA-NRMSE) while preserving the same offline pulse design principle as offered by UPs.

Optimal control gradient precision trade-offs: Application to fast generation of DeepControl libraries for MRI

We have recently demonstrated supervised deep learning methods for rapid generation of radiofrequency pulses in magnetic resonance imaging (https://doi.org/10.1002/mrm.27740, https://doi.org/10.1002/mrm.28667). Unlike the previous iterative optimization approaches, deep learning methods generate a pulse using a fixed number of floating-point operations - this is important in MRI, where patient-specific pulses preferably must be produced in real time. However, deep learning requires vast training libraries, which must be generated using the traditional methods, e.g., iterative quantum optimal control methods. Those methods are usually variations of gradient descent, and the calculation of the gradient of the performance metric with respect to the pulse waveform can be the most numerically intensive step. In this communication, we explore various ways in which the calculation of gradients in quantum optimal control theory may be accelerated. Four optimization avenues are explored: truncated commutator series expansions at zeroth and first order, a novel midpoint truncation scheme at first order, and the exact complex-step method. For the spin systems relevant to MRI, the first-order midpoint truncation is found to be sufficiently accurate, but also significantly faster than the machine precision gradient. This makes the generation of training databases for the machine learning methods considerably more realistic.

Performance analysis of integrated RF microstrip transmit antenna arrays with high channel count for body imaging at 7 T

The aim of the current study was to investigate the performance of integrated RF transmit arrays with high channel count consisting of meander microstrip antennas for body imaging at 7 T and to optimize the position and number of transmit elements. RF simulations using multiring antenna arrays placed behind the bore liner were performed for realistic exposure conditions for body imaging. Simulations were performed for arrays with as few as eight elements and for arrays with high channel counts of up to 48 elements. The B₁⁺  field was evaluated regarding the degrees of freedom for RF shimming in the abdomen. Worst-case specific absorption rate (SAR_wc ), SAR overestimation in the matrix compression, the number of virtual observation points (VOPs) and SAR efficiency were evaluated. Constrained RF shimming was performed in differently oriented regions of interest in the body, and the deviation from a target B₁⁺  field was evaluated. Results show that integrated multiring arrays are able to generate homogeneous B₁⁺ field distributions for large FOVs, especially for coronal/sagittal slices, and thus enable body imaging at 7 T with a clinical workflow; however, a low duty cycle or a high SAR is required to achieve homogeneous B₁⁺  distributions and to exploit the full potential. In conclusion, integrated arrays allow for high element counts that have high degrees of freedom for the pulse optimization but also produce high SAR_wc , which reduces the SAR accuracy in the VOP compression for low-SAR protocols, leading to a potential reduction in array performance. Smaller SAR overestimations can increase SAR accuracy, but lead to a high number of VOPs, which increases the computational cost for VOP evaluation and makes online SAR monitoring or pulse optimization challenging. Arrays with interleaved rings showed the best results in the study.

Local excitation universal parallel transmit pulses at 9.4T

PURPOSE

To demonstrate that the concept of "universal pTx pulses" is applicable to local excitation applications.

METHODS

A database of B₀ / B 1 + maps from eight different subjects was acquired at 9.4T. Based on these maps, universal pulses that aim at local excitation of the visual cortex area in the human brain (with a flip angle of 90° or 7°) were calculated. The remaining brain regions should not experience any excitation. The pulses were designed with an extension of the "spatial domain method." A 2D and a 3D target excitation pattern were tested, respectively. The pulse performance was examined on non-database subjects by Bloch simulations and in vivo at 9.4T using a GRE anatomical MRI and a presaturated TurboFLASH B 1 + mapping sequence.

RESULTS

The calculated universal pulses show excellent performance in simulations and in vivo on subjects that were not contained in the design database. The visual cortex region is excited, while the desired non-excitation areas produce the only minimal signal. In simulations, the pulses with 3D target pattern show a lack of excitation uniformity in the visual cortex region; however, in vivo, this inhomogeneity can be deemed acceptable. A reduced field of view application of the universal pulse design concept was performed successfully.

CONCLUSIONS

The proposed design approach creates universal local excitation pulses for a flip angle of 7° and 90°, respectively. Providing universal pTx pulses for local excitation applications prospectively abandons the need for time-consuming subject-specific B₀ / B 1 + mapping and pTx-pulse calculation during the scan session.

k-Space Domain Parallel Transmit Pulse Design

PURPOSE

To accelerate the design of (under- or oversampled) multidimensional parallel transmission pulses.

METHODS

A k-space domain parallel transmission pulse design algorithm was proposed that produces a sparse matrix relating a complex-valued target excitation pattern to the pulses that produce it, and can be finely parallelized. The algorithm was applied in simulations to the design of 3D SPINS pulses for inner volume excitation in the brain at 7 Tesla. It was characterized in terms of the dependence of computation time, excitation error, and required memory on algorithm parameters, and it was compared to an iterative spatial domain pulse design method in terms of computation time, excitation error, Gibbs ringing, and ability to compensate off-resonance.

RESULTS

The proposed algorithm achieved approximately 80% faster pulse design compared to the spatial domain method with the same number of parallel threads, with the tradeoff of increased excitation error and RMS RF amplitude. It reduced the memory required to store the design matrix by 99% compared to a full matrix solution. Even with a coarse design grid, the algorithm produced patterns that were free of Gibbs ringing. It was similarly sensitive to k-space undersampling as the spatial domain method, and was similarly capable of compensating for off-resonance.

CONCLUSIONS

The proposed k-space domain algorithm accelerates and finely parallelizes parallel transmission pulse design, with a modest tradeoff of excitation error and RMS RF amplitude.

Simultaneous optimization of radio frequency and gradient waveforms with exact Hessians and slew rate constraints applied to kT-points excitation

We consider an excitation pulse with piecewise constant gradient trajectories and radio frequency (RF) waveforms such that the solution of the Bloch equations without relaxation terms can be represented by rotations. Based on this analytic solution we formulate a non-linear program for finding sub-pulse durations, gradient strengths, and complex RF voltages which minimize the deviation between the achieved and desired magnetization. We develop explicit expressions for the first and second order derivatives of the objective function. We extend the non-linear program to precisely account for gradient slew rate constraints. Using an interior point solver we apply the developed theory to simultaneously optimize the positions of k_T-points, their associated RF voltages and durations.

Robust RF shimming and small-tip-angle multispoke pulse design with finite-difference regularization

PURPOSE

A new regularizer is proposed for the magnitude least-squares optimization algorithm, to ensure robust parallel transmit RF shimming and small-tip-angle multispoke pulse designs for ultrahigh-field MRI.

METHODS

A finite-difference regularization term is activated as an additional regularizer in the iterative magnitude-least-squares based pulse design algorithm when an unwanted flip angle null distribution is detected. Both simulated and experimental B 1 + maps from different transmit arrays and different human subjects at 7 T were used to evaluate the proposed algorithm. The algorithm was further demonstrated in experiment with dynamic multislice RF shimming for a single-shot gradient-echo EPI for human functional MRI at 7 T.

RESULTS

The proposed finite-difference regularizer effectively prevented excitation null to be formed for RF shimming and small-tip-angle multispoke pulses, and improved the latter with a monotonic trade-off relationship between flip angle error and RF power. The proposed algorithm was demonstrated to be effective with several head-array geometries by simulation and with a commercial head array with 12 healthy human subjects by experiment. During a functional MRI scan at 7 T with dynamic RF shimming, the proposed algorithm ensured high image SNR throughout the human brain, compared with near-complete local signal loss by the conventional magnitude-least-squares algorithm.

CONCLUSION

Using finite-difference regularization to avoid unwanted solutions, the robustness of RF shimming and small-tip-angle multispoke pulse design algorithms are improved, with better flip angle homogeneity and a monotonic trade-off relationship between flip angle error and RF power.

Improved 7 Tesla transmit field homogeneity with reduced electromagnetic power deposition using coupled Tic Tac Toe antennas

Recently cleared by the FDA, 7 Tesla (7 T) MRI is a rapidly growing technology that can provide higher resolution and enhanced contrast in human MRI images. However, the increased operational frequency (~ 297 MHz) hinders its full potential since it causes inhomogeneities in the images and increases the power deposition in the tissues. This work describes the optimization of an innovative radiofrequency (RF) head coil coupled design, named Tic Tac Toe, currently used in large scale human MRI scanning at 7 T; to date, this device was used in more than 1,300 neuro 7 T MRI scans. Electromagnetic simulations of the coil were performed using the finite-difference time-domain method. Numerical optimizations were used to combine the calculated electromagnetic fields produced by these antennas, based on the superposition principle, resulting in homogeneous magnetic field distributions at low levels of power deposition in the tissues. The simulations were validated in-vivo using the Tic Tac Toe RF head coil system on a 7 T MRI scanner.

Fast online-customized (FOCUS) parallel transmission pulses: A combination of universal pulses and individual optimization

PURPOSE

To mitigate spatial flip angle (FA) variations under strict specific absorption rate (SAR) constraints for ultra-high field MRI using a combination of universal parallel transmit (pTx) pulses and fast subject-specific optimization.

METHODS

Data sets consisting of B₀ , B 1 + maps, and virtual observation point (VOP) data were acquired from 72 subjects (study groups of 48/12 healthy Europeans/Asians and 12 Europeans with pathological or incidental findings) using an 8Tx/32Rx head coil on a 7T whole-body MR system. Combined optimization values (COV) were defined as combination of spiral-nonselective (SPINS) trajectory parameters and an energy regularization weight. A set of COV was optimized universally by simulating the individual RF pulse optimizations of 12 training data sets (healthy Europeans). Subsequently, corresponding universal pulses (UPs) were calculated. Using COV and UPs, individually optimized pulses (IOPs) were calculated during the sequence preparation phase (maximum 15 s). Two different UPs and IOPs were evaluated by calculating their normalized root-mean-square error (NRMSE) of the FA and SAR in simulations of all data sets. Seven additional subjects were examined using an MPRAGE sequence that uses the designed pTx excitation pulses and a conventional adiabatic inversion.

RESULTS

All pTx pulses resulted in decreased mean NRMSE compared to a circularly polarized (CP) pulse (CP = ~28%, UPs = ~17%, and IOPs = ~12%). UPs and IOPs improved homogeneity for all subjects. Differences in NRMSE between study groups were much lower than differences between different pulse types.

CONCLUSION

UPs can be used to generate fast online-customized (FOCUS) pulses gaining lower NRMSE and/or lower SAR values.

Application of Evolution Strategies to the Design of SAR Efficient Parallel Transmit Multi-Spoke Pulses for Ultra-High Field MRI

We present an evolution-strategy based approach to solve the magnitude least squares (MLS) design problem of low flip-angle slice-selective parallel transmit RF pulses for ultra-high field MRI using SAR and peak-RF-constraints. A combined transmit k-space trajectory and RF pulse weight optimization is proposed in two algorithmic steps. The first step is a coarse grid search to find an initial solution that fulfills all constraints for the subsequent multistage optimization. This avoids convergence to the next nearest local minimum. The second step attempts to refine the results using multiple evolution strategies. We compare the performance of our approach with the non-convex optimization methods described in the literature. The proposed algorithm converges for phantom and in vivo data and only requires an initial estimate of the range of suitable regularization parameters. It demonstrates improved excitation homogeneity compared to published spoke-design methods and allows optimization for homogeneity with a subsequent reduction in the SAR burden. Moreover, excitation homogeneity and the SAR burden can be balanced against each other, enabling a further reduction in SAR at the cost of minor relaxations in excitation homogeneity. This feature makes the algorithm a good candidate for SAR limited sequences in ultra-high field imaging. The algorithm is validated using phantom and in vivo measurements obtained with a 16-channel transmit array at 9.4T.

General gradient delay correction method in bipolar multispoke RF pulses using trim blips

PURPOSE

To correct with gradient trim blips for gradient delays in bipolar-spoke RF pulses in slice-selective and slab-selective excitations, compatible with tilted acquisitions and anisotropic delays.

THEORY

The effect of small gradient delays with respect to RF pulses results in a dephasing of the second RF spoke, proportional to the slab-selection gradient amplitude and the distance of the slice center from the magnet isocenter. Accordingly, adding a trim blip along the corresponding logical gradient axis between the two spokes compensates for the same dephasing, and therefore cancels the gradient delay effects, regardless of position and orientation.

METHODS

Gradient delays on different axes were first measured on a 7T system based on an imaging method. Parallel transmission universal bipolar spokes were designed offline to mitigate the RF field inhomogeneity problem in the human brain. Trim blips were used to compensate for the known delays, which was validated with flip angle and temporal SNR measurements on two different volunteers at 7 T.

RESULTS

Pulses corrected with trim blips greatly reduced gradient delay effects. Acquisitions made with corrected and noncorrected pulses showed good fidelity with simulations.

CONCLUSIONS

Unlike time or phase-shifting approaches, trim blip-based methods apply to all possible bipolar spoke scenarios such as slice excitations, slab excitations, and anisotropy in the gradient delays.

Universal nonselective excitation and refocusing pulses with improved robustness to off-resonance for Magnetic Resonance Imaging at 7 Tesla with parallel transmission

PURPOSE

In MRI at ultra-high field, the k T -point and spiral nonselective (SPINS) pulse design techniques can be advantageously combined with the parallel transmission (pTX) and universal pulse techniques to create uniform excitation in a calibration-free manner. However, in these approaches, pulse duration is typically increased as compared to standard hard pulses, and excitation quality in regions exhibiting large resonance frequency offsets often suffer. This limitation is inherent to structure of k T -point or SPINS pulse, and likely can be mitigated using parameterization-free pulse design approaches.

METHODS

The Gradient Ascent Pulse Engineering (GRAPE) algorithm was used to design parameterization-free RF and magnetic field gradient (MFG) waveforms for creating 8 ∘ excitation, up to 105 ∘ scalable refocusing and inversion, nonselectively across the brain. Simulations were performed to provide flip angle normalized root-mean-squares error (FA-NRMSE) estimations for the 8 ∘ and the 180 ∘ k T -point, SPINS, and GRAPE pulses. GRAPE pulses were tested experimentally with anatomical head scans at 7T.

RESULTS

As compared to k T -points and SPINS, GRAPE provided substantial improvement of excitation, refocusing, and inversion quality at off-resonance while at least preserving the same global FA-NRMSE performance. As compared to k T -points, GRAPE allowed for a substantial reduction of the pulse duration for the 8 ∘ excitation and the 105 ∘ refocusing.

CONCLUSIONS

Parameterization-free universal nonselective pTX-pulses were successfully computed using GRAPE. Performance gains as compared to k T -points were validated numerically and experimentally for three imaging protocols. In its current implementation, the computational burden of GRAPE limits its use to applications where pulse computations are not subject to time constraints.

Improving PCASL at ultra-high field using a VERSE-guided parallel transmission strategy

Purpose

To improve the labeling efficiency of pseudo‐continuous arterial spin labeling (PCASL) at 7T using parallel transmission (pTx).

Methods

Five healthy subjects were scanned on an 8‐channel‐transmit 7T human MRI scanner. Time‐of‐flight (TOF) angiography was acquired to identify regions of interest (ROIs) around the 4 major feeding arteries to the brain, and B1+ and B₀ maps were acquired in the labeling plane for tagging pulse design. Complex weights of the labeling pulses for each of the 8 transmit channels were calculated to produce a homogenous radiofrequency (RF) ‐shimmed labeling across the ROIs. Variable‐Rate Selective Excitation (VERSE) pulses were also implemented as a part of the labeling pulse train. Whole‐brain perfusion‐weighted images were acquired under conditions of RF shimming, VERSE with RF shimming, and standard circularly polarized (CP) mode. The same subjects were scanned on a 3T scanner for comparison.

Results

In simulation, VERSE with RF shimming improved the flip‐angles across the ROIs in the labeling plane by 90% compared with CP mode. VERSE with RF shimming improved the temporal signal‐to‐noise ratio by 375% compared with CP mode, but did not outperform a matched 3T sequence with a matched flip‐angle.

Conclusion

We have demonstrated improved PCASL tagging at 7T using VERSE with RF shimming on a commercial head coil under conservative SAR limits at 7T. However, improvements of 7T over 3T may require strategies with less conservative SAR restrictions.

IMPULSE: A scalable algorithm for design of minimum specific absorption rate parallel transmit RF pulses

PURPOSE

Managing local specific absorption rate (SAR) in parallel transmission requires ensuring that the peak SAR over a large number of voxels (> 10 5 ) is below the regulatory limit. The safety risk to the patient depends on cumulative (not instantaneous) SAR thus making a joint design of all RF pulses in a sequence desirable. We propose the Iterative Minimization Procedure with Uncompressed Local SAR Estimate (IMPULSE), an efficient optimization formulation and algorithm that can handle uncompressed SAR matrices and optimize pulses for all slices jointly within a practical time frame.

THEORY AND METHODS

IMPULSE optimizes parallel transmit pulses for small-tip-angle slice selective excitation to minimize a single cost function incorporating multiple quantities (local SAR, global SAR, and per-channel power) averaged over the entire multislice scan subject to a strict constraint on excitation accuracy. Pulses for an 8-channel 7T head coil were designed with IMPULSE and compared with pulses designed using generic optimization algorithms and VOPs to assess the computation time and SAR performance benefits.

RESULTS

IMPULSE achieves lower SAR and shorter computation time compared with a VOP approach. Compared with the generic sequential quadratic programming algorithm, computation time is reduced by a factor of 5-6 by using IMPULSE. Using as many as 6 million local SAR terms, up to 120 slices can be designed jointly with IMPULSE within 45 s.

CONCLUSIONS

IMPULSE can handle significantly larger number of SAR matrices and slices than conventional optimization algorithms, enabling the use of uncompressed or partially compressed SAR matrices to design pulses for a multislice scan in a practical time frame.

Human Connectome Project-style resting-state functional MRI at 7 Tesla using radiofrequency parallel transmission

We investigate the utility of radiofrequency (RF) parallel transmission (pTx) for whole-brain resting-state functional MRI (rfMRI) acquisition at 7 Tesla (7T). To this end, Human Connectome Project (HCP)-style data acquisitions were chosen as a showcase example. Five healthy subjects were scanned in pTx and single-channel transmit (1Tx) modes. The pTx data were acquired using a prototype 16-channel transmit system and a commercially available Nova 8-channel transmit 32-channel receive RF head coil. Additionally, pTx single-spoke multiband (MB) pulses were designed to image sagittal slices. HCP-style 7T rfMRI data (1.6-mm isotropic resolution, 5-fold slice and 2-fold in-plane acceleration, 3600 image volumes and ∼ 1-h scan) were acquired with pTx and the results were compared to those acquired with the original 7T HCP rfMRI protocol. The use of pTx significantly improved flip-angle uniformity across the brain, with coefficient of variation (i.e., std/mean) of whole-brain flip-angle distribution reduced on average by ∼39%. This in turn yielded ∼17% increase in group temporal SNR (tSNR) as averaged across the entire brain and ∼10% increase in group functional contrast-to-noise ratio (fCNR) as averaged across the grayordinate space (including cortical surfaces and subcortical voxels). Furthermore, when placing a seed in either the posterior parietal lobe or putamen to estimate seed-based dense connectome, the increase in fCNR was observed to translate into stronger correlation of the seed with the rest of the grayordinate space. We have demonstrated the utility of pTx for slice-accelerated high-resolution whole-brain rfMRI at 7T; as compared to current state-of-the-art, the use of pTx improves flip-angle uniformity, increases tSNR, enhances fCNR and strengthens functional connectivity estimation.

High-resolution whole-brain diffusion MRI at 7T using radiofrequency parallel transmission

PURPOSE

Investigating the utility of RF parallel transmission (pTx) for Human Connectome Project (HCP)-style whole-brain diffusion MRI (dMRI) data at 7 Tesla (7T).

METHODS

Healthy subjects were scanned in pTx and single-transmit (1Tx) modes. Multiband (MB), single-spoke pTx pulses were designed to image sagittal slices. HCP-style dMRI data (i.e., 1.05-mm resolutions, MB2, b-values = 1000/2000 s/mm² , 286 images and 40-min scan) and data with higher accelerations (MB3 and MB4) were acquired with pTx.

RESULTS

pTx significantly improved flip-angle detected signal uniformity across the brain, yielding ∼19% increase in temporal SNR (tSNR) averaged over the brain relative to 1Tx. This allowed significantly enhanced estimation of multiple fiber orientations (with ∼21% decrease in dispersion) in HCP-style 7T dMRI datasets. Additionally, pTx pulses achieved substantially lower power deposition, permitting higher accelerations, enabling collection of the same data in 2/3 and 1/2 the scan time or of more data in the same scan time.

CONCLUSION

pTx provides a solution to two major limitations for slice-accelerated high-resolution whole-brain dMRI at 7T; it improves flip-angle uniformity, and enables higher slice acceleration relative to current state-of-the-art. As such, pTx provides significant advantages for rapid acquisition of high-quality, high-resolution truly whole-brain dMRI data.

Machine learning RF shimming: Prediction by iteratively projected ridge regression

PURPOSE

To obviate online slice-by-slice RF shim optimization and reduce B1+ mapping requirements for patient-specific RF shimming in high-field magnetic resonance imaging.

THEORY AND METHODS

RF Shim Prediction by Iteratively Projected Ridge Regression (PIPRR) predicts patient-specific, SAR-efficient RF shims with a machine learning approach that merges learning with training shim design. To evaluate it, a set of B1+ maps was simulated for 100 human heads for a 24-element coil at 7T. Features were derived from tissue masks and the DC Fourier coefficients of the coils' B1+ maps in each slice, which were used for kernelized ridge regression prediction of SAR-efficient RF shim weights. Predicted shims were compared to directly designed shims, circularly polarized mode, and nearest-neighbor shims predicted using the same features.

RESULTS

PIPRR predictions had 87% and 13% lower B1+ coefficients of variation compared to circularly polarized mode and nearest-neighbor shims, respectively, and achieved homogeneity and SAR similar to that of directly designed shims. Predictions were calculated in 4.92 ms on average.

CONCLUSION

PIPRR predicted uniform, SAR-efficient RF shims, and could save a large amount of B1+ mapping and computation time in RF-shimmed ultra-high field magnetic resonance imaging.

Rotation relaxation splitting for optimizing parallel RF excitation pulses with T1- and T2-relaxations in MRI

Exact solutions of the Bloch equations with T₁- and T₂-relaxation terms for piecewise constant magnetic fields are numerically challenging. We therefore investigate an approximation for the achieved magnetization in which rotations and relaxations are split into separate operations. We develop an estimate for its accuracy and explicit first and second order derivatives with respect to the complex excitation radio frequency voltages. In practice, the deviation between an exact solution of the Bloch equations and this rotation relaxation splitting approximation seems negligible. Its computation times are similar to exact solutions without relaxation terms. We apply the developed theory to numerically optimize radio frequency excitation waveforms with T₁- and T₂-relaxations in several examples.

Whole-brain 3D FLAIR at 7T using direct signal control

Purpose

Image quality obtained for brain imaging at 7T can be hampered by inhomogeneities in the static magnetic field, B₀, and the RF electromagnetic field, B₁. In imaging sequences such as fluid‐attenuated inversion recovery (FLAIR), which is used to assess neurological disorders, these inhomogeneities cause spatial variations in signal that can reduce clinical efficacy. In this work, we aim to correct for signal inhomogeneities to ensure whole‐brain coverage with 3D FLAIR at 7T.

Methods

The direct signal control (DSC) framework was used to optimize channel weightings applied to the 8 transmit channels used in this work on a pulse‐by‐pulse basis through the echo train in the FLAIR sequences. 3D FLAIR brain images were acquired on 5 different subjects and compared with imaging using a quadrature‐like mode of the transmit array. Precomputed “universal” DSC solutions calculated from a separate set of 5 subjects were also explored.

Results

DSC consistently enabled improved imaging across all subjects, with no dropouts in signal seen over the entire brain volume, which contrasted with imaging in quadrature mode. Further, the universal DSC solutions also consistently improved imaging despite not being optimized specifically for the subject being imaged.

Conclusion

3D FLAIR brain imaging at 7T is substantially improved using DSC and is able to recover regions of low signal without increasing imaging time or interecho spacing.

Designing 3D selective adiabatic radiofrequency pulses with single and parallel transmission

PURPOSE

To introduce a method of designing single and parallel transmit (pTx) 3D adiabatic π pulses for inverting and refocusing spins that are insensitive to transmit B1 ( B1+) inhomogeneity.

THEORY AND METHODS

A 3D adiabatic pulse is created by replacing each piece-wise constant element (or sub-pulse) of an adiabatic full passage (AFP) by a 2D selective pulse. In this study, the parent AFP is an HS1 and each sub-pulse is a 2D pulse derived from a jinc function designed using a spiral k-trajectory. Spatial selectivity in the third direction is achieved by blipping the slab-selective gradient between sub-pulses, yielding a rectangular slab profile identical to that of the parent AFP. The slew-rate limited sub-pulse can be undersampled utilizing pTx, thus shortening the overall pulse width. Simulations and experiments demonstrate the quality of spatial selectivity and adiabaticity achievable.

RESULTS

The 3D adiabatic pulse inverts and refocus spins in a sharply demarcated cylindrical volume. When stepping RF amplitude, an adiabatic threshold is observed above which the flip angle remains π. Experimental results demonstrate that pTx is an effective means to significantly improve pulse performance.

CONCLUSION

A method of designing 3D adiabatic pulses insensitive to B1 inhomogeneity has been developed. pTx can shorten these pulses while retaining their adiabatic character. Magn Reson Med 79:701-710, 2018. © 2017 International Society for Magnetic Resonance in Medicine.

Design of universal parallel-transmit refocusing kT -point pulses and application to 3D T2 -weighted imaging at 7T

PURPOSE

T₂ -weighted sequences are particularly sensitive to the radiofrequency (RF) field inhomogeneity problem at ultra-high-field because of the errors accumulated by the imperfections of the train of refocusing pulses. As parallel transmission (pTx) has proved particularly useful to counteract RF heterogeneities, universal pulses were recently demonstrated to save precious time and computational efforts by skipping B₁ calibration and online RF pulse tailoring. Here, we report a universal RF pulse design for non-selective refocusing pulses to mitigate the RF inhomogeneity problem at 7T in turbo spin-echo sequences with variable flip angles.

METHOD

Average Hamiltonian theory was used to synthetize a single non-selective refocusing pulse with pTx while optimizing its scaling properties in the presence of static field offsets. The design was performed under explicit power and specific absorption rate constraints on a database of 10 subjects using a 8Tx-32Rx commercial coil at 7T. To validate the proposed design, the RF pulses were tested in simulation and applied in vivo on 5 additional test subjects.

RESULTS

The root-mean-square rotation angle error (RA-NRMSE) evaluation and experimental data demonstrated great improvement with the proposed universal pulses (RA-NRMSE ∼8%) compared to the standard circularly polarized mode of excitation (RA-NRMSE ∼26%).

CONCLUSION

This work further completes the spectrum of 3D universal pulses to mitigate RF field inhomogeneity throughout all 3D MRI sequences without any pTx calibration. The approach returns a single pulse that can be scaled to match the desired flip angle train, thereby increasing the modularity of the proposed plug and play approach. Magn Reson Med 80:53-65, 2018. © 2017 International Society for Magnetic Resonance in Medicine.

Advancing RF pulse design using an open-competition format: Report from the 2015 ISMRM challenge

PURPOSE

To advance the best solutions to two important RF pulse design problems with an open head-to-head competition.

METHODS

Two sub-challenges were formulated in which contestants competed to design the shortest simultaneous multislice (SMS) refocusing pulses and slice-selective parallel transmission (pTx) excitation pulses, subject to realistic hardware and safety constraints. Short refocusing pulses are needed for spin echo SMS imaging at high multiband factors, and short slice-selective pTx pulses are needed for multislice imaging in ultra-high field MRI. Each sub-challenge comprised two phases, in which the first phase posed problems with a low barrier of entry, and the second phase encouraged solutions that performed well in general. The Challenge ran from October 2015 to May 2016.

RESULTS

The pTx Challenge winners developed a spokes pulse design method that combined variable-rate selective excitation with an efficient method to enforce SAR constraints, which achieved 10.6 times shorter pulse durations than conventional approaches. The SMS Challenge winners developed a time-optimal control multiband pulse design algorithm that achieved 5.1 times shorter pulse durations than conventional approaches.

CONCLUSION

The Challenge led to rapid step improvements in solutions to significant problems in RF excitation for SMS imaging and ultra-high field MRI. Magn Reson Med 78:1352-1361, 2017. © 2016 International Society for Magnetic Resonance in Medicine.

Homogeneous non-selective and slice-selective parallel-transmit excitations at 7 Tesla with universal pulses: A validation study on two commercial RF coils

Parallel transmission (pTx) technology, despite its great potential to mitigate the transmit field inhomogeneity problem in magnetic resonance imaging at ultra-high field (UHF), suffers from a cumbersome calibration procedure, thereby making the approach problematic for routine use. The purpose of this work is to demonstrate on two different 7T systems respectively equipped with 8-transmit-channel RF coils from two different suppliers (Rapid-Biomed and Nova Medical), the benefit of so-called universal pulses (UP), optimized to produce uniform excitations in the brain in a population of adults and making unnecessary the calibration procedures mentioned above. Non-selective and slice-selective UPs were designed to return homogeneous excitation profiles throughout the brain simultaneously on a group of ten subjects, which then were subsequently tested on ten additional volunteers in magnetization prepared rapid gradient echo (MPRAGE) and multi-slice gradient echo (2D GRE) protocols. The results were additionally compared experimentally with the standard non-pTx circularly-polarized (CP) mode, and in simulation with subject-specific tailored excitations. For both pulse types and both coils, the UP mode returned a better signal and contrast homogeneity than the CP mode. Retrospective analysis of the flip angle (FA) suggests that the FA deviation from the nominal FA on average over a healthy adult population does not exceed 11% with the calibration-free parallel-transmit pulses whereas it goes beyond 25% with the CP mode. As a result the universal pulses designed in this work confirm their relevance in 3D and 2D protocols with commercially available equipment. Plug-and-play pTx implementations henceforth become accessible to exploit with more flexibility the potential of UHF for brain imaging.

Extended RF shimming: Sequence-level parallel transmission optimization applied to steady-state free precession MRI of the heart

Cardiac magnetic resonance imaging (MRI) at high field presents challenges because of the high specific absorption rate and significant transmit field (B₁⁺ ) inhomogeneities. Parallel transmission MRI offers the ability to correct for both issues at the level of individual radiofrequency (RF) pulses, but must operate within strict hardware and safety constraints. The constraints are themselves affected by sequence parameters, such as the RF pulse duration and TR, meaning that an overall optimal operating point exists for a given sequence. This work seeks to obtain optimal performance by performing a 'sequence-level' optimization in which pulse sequence parameters are included as part of an RF shimming calculation. The method is applied to balanced steady-state free precession cardiac MRI with the objective of minimizing TR, hence reducing the imaging duration. Results are demonstrated using an eight-channel parallel transmit system operating at 3 T, with an in vivo study carried out on seven male subjects of varying body mass index (BMI). Compared with single-channel operation, a mean-squared-error shimming approach leads to reduced imaging durations of 32 ± 3% with simultaneous improvement in flip angle homogeneity of 32 ± 8% within the myocardium.

SAR Simulations & Safety

At ultra-high fields, the assessment of radiofrequency (RF) safety presents several new challenges compared to low-field systems. Multi-channel RF transmit coils in combination with parallel transmit techniques produce time-dependent and spatially varying power loss densities in the tissue. Further, in ultra-high-field systems, localized field effects can be more pronounced due to a transition from the quasi stationary to the electromagnetic field regime. Consequently, local information on the RF field is required for reliable RF safety assessment as well as for monitoring of RF exposure during MR examinations. Numerical RF and thermal simulations for realistic exposure scenarios with anatomical body models are currently the only practical way to obtain the requisite local information on magnetic and electric field distributions as well as tissue temperature. In this article, safety regulations and the fundamental characteristics of RF field distributions in ultra-high-field systems are reviewed. Numerical methods for computation of RF fields as well as typical requirements for the analysis of realistic multi-channel RF exposure scenarios including anatomical body models are highlighted. In recent years, computation of the local tissue temperature has become of increasing interest, since a more accurate safety assessment is expected because temperature is directly related to tissue damage. Regarding thermal simulation, bio-heat transfer models and approaches for taking into account the physiological response of the human body to RF exposure are discussed. In addition, suitable methods are presented to validate calculated RF and thermal results with measurements. Finally, the concept of generalized simulation-based specific absorption rate (SAR) matrix models is discussed. These models can be incorporated into local SAR monitoring in multi-channel MR systems and allow the design of RF pulses under constraints for local SAR.

Local SAR, global SAR, and power-constrained large-flip-angle pulses with optimal control and virtual observation points

PURPOSE

To present a constrained optimal-control (OC) framework for designing large-flip-angle parallel-transmit (pTx) pulses satisfying hardware peak-power as well as regulatory local and global specific-absorption-rate (SAR) limits. The application is 2D and 3D spatial-selective 90° and 180° pulses.

THEORY AND METHODS

The OC gradient-ascent-pulse-engineering method with exact gradients and the limited-memory Broyden-Fletcher-Goldfarb-Shanno method is proposed. Local SAR is constrained by the virtual-observation-points method. Two numerical models facilitated the optimizations, a torso at 3 T and a head at 7 T, both in eight-channel pTx coils and acceleration-factors up to 4.

RESULTS

The proposed approach yielded excellent flip-angle distributions. Enforcing the local-SAR constraint, as opposed to peak power alone, reduced the local SAR 7 and 5-fold with the 2D torso excitation and inversion pulse, respectively. The root-mean-square errors of the magnetization profiles increased less than 5% with the acceleration factor of 4.

CONCLUSION

A local and global SAR, and peak-power constrained OC large-flip-angle pTx pulse design was presented, and numerically validated for 2D and 3D spatial-selective 90° and 180° pulses at 3 T and 7 T. Magn Reson Med 77:374-384, 2017. © 2015 Wiley Periodicals, Inc.

High-resolution gradient-recalled echo imaging at 9.4T using 16-channel parallel transmit simultaneous multislice spokes excitations with slice-by-slice flip angle homogenization

Purpose

In order to fully benefit from the improved signal‐to‐noise and contrast‐to‐noise ratios at 9.4T, the challenges of B1+ inhomogeneity and the long acquisition time of high‐resolution 2D gradient‐recalled echo (GRE) imaging were addressed.

Theory and Methods

Flip angle homogenized excitations were achieved by parallel transmission (pTx) of 3‐spoke pulses, designed by magnitude least‐squares optimization in a slice‐by‐slice fashion; the acquisition time reduction was achieved by simultaneous multislice (SMS) pulses. The slice‐specific spokes complex radiofrequency scaling factors were applied to sinc waveforms on a per‐channel basis and combined with the other pulses in an SMS slice group to form the final SMS‐pTX pulse. Optimal spokes locations were derived from simulations.

Results

Flip angle maps from presaturation TurboFLASH showed improvement of flip angle homogenization with 3‐spoke pulses over CP‐mode excitation (normalized root‐mean‐square error [NRMSE] 0.357) as well as comparable excitation homogeneity across the single‐band (NRMSE 0.119), SMS‐2 (NRMSE 0.137), and SMS‐3 (NRMSE 0.132) 3‐spoke pulses. The application of the 3‐spoke SMS‐3 pulses in a 48‐slice GRE protocol, which has an in‐plane resolution of 0.28 × 0.28 mm, resulted in a 50% reduction of scan duration (total acquisition time 6:52 min including reference scans).

Conclusion

Time‐efficient flip angle homogenized high‐resolution GRE imaging at 9.4T was accomplished by using slice‐specific SMS‐pTx spokes excitations. Magn Reson Med 78:1050–1058, 2017. © 2016 The Authors Magnetic Resonance in Medicine published by Wiley Periodicals, Inc. on behalf of International Society for Magnetic Resonance in Medicine.

In vivo demonstration of whole-brain multislice multispoke parallel transmit radiofrequency pulse design in the small and large flip angle regimes at 7 Tesla

PURPOSE

A multispoke specific absorption rate (SAR) -aware pulse design approach for homogeneous multiple-slice small and large flip angle (FA) excitations with parallel transmission is proposed. The approach aims at optimizing in a slice-specific manner the spokes locations and radiofrequency pulses.

METHODS

The problem is posed as a set of slice-specific magnitude-least-squares problems, linked together by hardware and SAR constraints, and solved jointly using an active-set algorithm. Average Hamiltonian theory is exploited in the large FA case to greatly reduce the computational burden. The approach is validated numerically by means of simulations and experimentally on two volunteers at 7 Tesla through application of a high-resolution T2*-weighted brain imaging protocol.

RESULTS

The optimization of up to 1300 variables under 745 explicit constraints could be performed in less than 1 and 4 min for the small and large FA cases, respectively. The joint design proves valuable for SAR demanding protocols. Compared with the conventional circularly polarized mode, the designed pulses increased the signal by more than 40% in 70% of the voxels.

CONCLUSION

The B1+ inhomogeneity problem was mitigated efficiently in a multislice near whole-brain coverage protocol in the small and large FA regimes using a rapid slice-specific pulse design algorithm where the pulses were optimized jointly. Magn Reson Med 78:1009-1019, 2017. © 2016 International Society for Magnetic Resonance in Medicine.

Toward imaging the body at 10.5 tesla

PURPOSE

To explore the potential of performing body imaging at 10.5 Tesla (T) compared with 7.0T through evaluating the transmit/receive performance of similarly configured dipole antenna arrays.

METHODS

Fractionated dipole antenna elements for 10.5T body imaging were designed and evaluated using numerical simulations. Transmit performance of antenna arrays inside the prostate, kidneys and heart were investigated and compared with those at 7.0T using both phase-only radiofrequency (RF) shimming and multi-spoke pulses. Signal-to-noise ratio (SNR) comparisons were also performed. A 10-channel antenna array was constructed to image the abdomen of a swine at 10.5T. Numerical methods were validated with phantom studies at both field strengths.

RESULTS

Similar power efficiencies were observed inside target organs with phase-only shimming, but RF nonuniformity was significantly higher at 10.5T. Spokes RF pulses allowed similar transmit performance with accompanying local specific absorption rate increases of 25-90% compared with 7.0T. Relative SNR gains inside the target anatomies were calculated to be >two-fold higher at 10.5T, and 2.2-fold SNR gain was measured in a phantom. Gradient echo and fast spin echo imaging demonstrated the feasibility of body imaging at 10.5T with the designed array.

CONCLUSION

While comparable power efficiencies can be achieved using dipole antenna arrays with static shimming at 10.5T; increasing RF nonuniformities underscore the need for efficient, robust, and safe parallel transmission methods. Magn Reson Med 77:434-443, 2017. © 2016 International Society for Magnetic Resonance in Medicine.

Array-compressed parallel transmit pulse design

PURPOSE

To design array-compressed parallel transmit radiofrequency (RF) pulses and compare them to pulses designed with existing transmit array compression strategies.

THEORY AND METHODS

Array-compressed parallel RF pulse design is proposed as the joint optimization of a matrix of complex-valued compression weights that relate a full-channel physical array to a reduced-channel virtual array, along with a set of RF pulses for the virtual array. In this way, the physics of the RF pulse application determine the coil combination weights. Array-compressed pulse design algorithms are described for four parallel transmit applications: accelerated two-dimensional spiral excitation, multislice RF shimming, small-tip-angle kT -points excitation, and slice-selective spokes refocusing. Array-compressed designs are compared in simulations and an experiment to pulses designed using four existing array compression strategies.

RESULTS

In all cases, array-compressed pulses achieved the lowest root-mean-square excitation error among the array compression approaches. Low errors were generally achieved without increasing root-mean-square RF amplitudes or maximum local 10-gram specific absorption rate. Leave-one-out multisubject shimming simulations demonstrated that array-compressed RF shimming can identify useful fixed coil combination weights that perform well across a population.

CONCLUSION

Array-compressed pulse design jointly identifies the transmit coil array compression weights and RF pulses that perform best for a specific parallel excitation application. Magn Reson Med 76:1158-1169, 2016. © 2015 Wiley Periodicals, Inc.

Probabilistic analysis of the specific absorption rate intersubject variability safety factor in parallel transmission MRI

PURPOSE

Specific absorption rate (SAR) calculations in parallel transmission are commonly performed by using electromagnetic simulations on generic models. In this study, we propose a probabilistic analysis to study the safety factor employed to account for SAR intersubject variability versus risk relationship in head imaging at 7T.

METHODS

Thirty-three finite-element electromagnetic simulations were conducted to sample the four-dimensional parameter space consisting of the head length, head breadth, and shifts in Z and Y random variables. Based on the SAR matrices for each configuration, a multivariate second-order polynomial of the SAR versus the different parameters was reconstructed for different types of radiofrequency pulses. A Monte Carlo calculation was then performed to compute the probability of occurrence of a given SAR value.

RESULTS

By testing a large number of radiofrequency excitation pulses, the SAR calculated for the average model amplified by a safety margin of 1.5 was found to return a probability of less than 1% to be exceeded across the adult Caucasian population given the investigated parameters.

CONCLUSION

The proposed method to study SAR intersubject variability uses a reasonable number of electromagnetic simulations. Look-ahead SAR safety margins can be deduced based on risk/benefit ratio assessments. Magn Reson Med 78:1217-1223, 2017. © 2016 International Society for Magnetic Resonance in Medicine.

Robust time-shifted spoke pulse design in the presence of large B0 variations with simultaneous reduction of through-plane dephasing, B1+ effects, and the specific absorption rate using parallel transmission

PURPOSE

To design parallel transmission spokes pulses with time-shifted profiles for joint mitigation of intensity variations due to B1+ effects, signal loss due to through-plane dephasing, and the specific absorption rate (SAR) at 7T.

METHODS

We derived a slice-averaged small tip angle (SA-STA) approximation of the magnetization signal at echo time that depends on the B1+ transmit profiles, the through-slice B0 gradient and the amplitude and time-shifts of the spoke waveforms. We minimize a magnitude least-squares objective based on this signal equation using a fast interior-point approach with analytical expressions of the Jacobian and Hessian.

RESULTS

Our algorithm runs in less than three minutes for the design of two-spoke pulses subject to hundreds of local SAR constraints. On a B0/B1+ head phantom, joint optimization of the channel-dependent time-shifts and spoke amplitudes allowed signal recovery in high-B0 regions at no increase of SAR. Although the method creates uniform magnetization profiles (ie, uniform intensity), the flip angle varies across the image, which makes it ill-suited to T1-weighted applications.

CONCLUSIONS

The SA-STA approach presented in this study is best suited to T2*-weighted applications with long echo times that require signal recovery around high B0 regions. Magn Reson Med 76:540-554, 2016. © 2015 Wiley Periodicals, Inc.

Subject- and resource-specific monitoring and proactive management of parallel radiofrequency transmission

PURPOSE

Develop a practical comprehensive package for proactive management of parallel radiofrequency (RF) transmission.

METHODS

With a constrained optimization framework and predictive models from a prescan based multichannel calibration, we presented a method supporting design and optimization of parallel RF excitation pulses that accurately obey the forward/reflected peak and average power limits of the RF power amplifiers in parallel transmit imaging experiments and Bloch simulations. Moreover, local SAR limits were incorporated into the parallel RF excitation pulses using electromagnetic field simulations. Virtual transmit coils concept for minimization of reflected power (effecting subject-specific matching) was additionally demonstrated by leveraging experimentally calibrated power models.

RESULTS

Incorporation of experimentally calibrated power prediction models resulted in accurate compliance with prescribed hardware and global specific absorption rate (SAR) limits. Incorporation of spatial average 10 g SAR models, facilitated by simplifying numerical approximations, provided assurance of patient safety. RF pulses designed with various constraints demonstrated excellent excitation fidelity-the normalized root-mean-square error of the simulated excitation profiles was 2.6% for the fully constrained pulses, comparable to that of the unconstrained pulses. An RF shimming example showed a reduction of the reflected-to-forward power ratio to 1.7% from a conventional approach's 8.1%.

CONCLUSION

Using the presented RF pulse design method, effective proactive management of the multifaceted power and SAR limits was demonstrated in experimental and simulation studies. Magn Reson Med 76:20-31, 2016. © 2015 Wiley Periodicals, Inc.

Distributing coil elements in three dimensions enhances parallel transmission multiband RF performance: A simulation study in the human brain at 7 Tesla

PURPOSE

We explore the advantages of using a double-ring radiofrequency (RF) array and slice orientation to design parallel transmission (pTx) multiband (MB) pulses for simultaneous multislice (SMS) imaging with whole-brain coverage at 7 Tesla (T).

METHODS

A double-ring head array with 16 elements split evenly in two rings stacked in the z-direction was modeled and compared with two single-ring arrays consisting of 8 or 16 elements. The array performance was evaluated by designing band-specific pTx MB pulses with local specific absorption rate (SAR) control. The impact of slice orientations was also investigated.

RESULTS

The double-ring array consistently and significantly outperformed the other two single-ring arrays, with peak local SAR reduced by up to 40% at a fixed excitation error of 0.024. For all three arrays, exciting sagittal or coronal slices yielded better RF performance than exciting axial or oblique slices.

CONCLUSIONS

A double-ring RF array can be used to drastically improve SAR versus excitation fidelity tradeoff for pTx MB pulse design for brain imaging at 7 T; therefore, it is preferable against single-ring RF array designs when pursuing various biomedical applications of pTx SMS imaging. In comparing the stripline arrays, coronal and sagittal slices are more advantageous than axial and oblique slices for pTx MB pulses. Magn Reson Med 75:2464-2472, 2016. © 2016 Wiley Periodicals, Inc.

Parallel transmission pulse design with explicit control for the specific absorption rate in the presence of radiofrequency errors

PURPOSE

A new framework for the design of parallel transmit (pTx) pulses is presented introducing constraints for local and global specific absorption rate (SAR) in the presence of errors in the radiofrequency (RF) transmit chain.

METHODS

The first step is the design of a pTx RF pulse with explicit constraints for global and local SAR. Then, the worst possible SAR associated with that pulse due to RF transmission errors ("worst-case SAR") is calculated. Finally, this information is used to re-calculate the pulse with lower SAR constraints, iterating this procedure until its worst-case SAR is within safety limits.

RESULTS

Analysis of an actual pTx RF transmit chain revealed amplitude errors as high as 8% (20%) and phase errors above 3° (15°) for spokes (spiral) pulses. Simulations show that using the proposed framework, pulses can be designed with controlled "worst-case SAR" in the presence of errors of this magnitude at minor cost of the excitation profile quality.

CONCLUSION

Our worst-case SAR-constrained pTx design strategy yields pulses with local and global SAR within the safety limits even in the presence of RF transmission errors. This strategy is a natural way to incorporate SAR safety factors in the design of pTx pulses. Magn Reson Med 75:2493-2504, 2016. © 2015 Wiley Periodicals, Inc.

Universal pulses: A new concept for calibration-free parallel transmission

PURPOSE

A calibration-free parallel transmission method is investigated to mitigate the radiofrequency (RF) field inhomogeneity problem in brain imaging at 7 Tesla (T).

THEORY AND METHODS

Six volunteers were scanned to build a representative database of RF and static field maps at 7T. Small-tip-angle and inversion pulses were designed with joint k_T -points trajectory optimization to work robustly on all six subjects. The returned "universal" pulses were then inserted in an MPRAGE sequence implemented on six additional volunteers without further field measurements and pulse optimizations. Similar acquisitions were performed in the circularly polarized mode and with subject-based optimizations for comparison. Performance of the different approaches was evaluated by means of image analysis and computation of the flip angle normalized root mean square errors (NRMSE).

RESULTS

For both the excitation and inversion, the universal pulses (NRMSE∼11%) outperformed the circularly polarized (NRMSE∼28%) and RF shim modes (NRMSE∼20%) across all volunteers and returned slightly worse results than for subject-based optimized pulses (NRMSE∼7%).

CONCLUSION

RF pulses can be designed to robustly mitigate the RF field inhomogeneity problem over a population class. This appears as a first step toward another plug and play parallel transmission solution where the pulse design can be done offline and without measuring subject-specific field maps. Magn Reson Med 77:635-643, 2017. © 2016 International Society for Magnetic Resonance in Medicine.